The parents of 59 percent of black New York City elementary-school children opt out of their neighborhood school, aiming for a better one. That’s up from 38 percent a decade ago.

This damning statistic from last week’s New School study on school choice exposes the absurdity of new Chancellor Richard Carranza’s vow that “all students will be supported” as he aims to desegregate the system.

In all, the report notes, 40 percent of city kindergartners don’t attend the school they’re zoned for. A third go a fair distance “outside the community school district, usually toward higher-income neighborhoods.”

The study suggests this harms the schools these families are freed from by leaving them with reduced resources. In fact, that’s not how the funding formulas work. For example, the drop from 496 to 430 kids at PS 376 in Brooklyn, a school the researchers claim is harmed by choice, left it with an extra $3,400-plus per child.

And the kids who flee also win. Black elementary students wind up at schools with higher pass rates in both English (40 percent passing vs. 26 percent) and math (41 percent vs. 23 percent).

Yes, that’s only a marginal improvement — but that’s because the system simply doesn’t have enough good schools. Mayor de Blasio himself acknowledged the problem Thursday, addressing the controversy over desegregation plans: “If we try and solve the [diversity] problem without improving the schools, we actually will not be getting where we need to be.”

This is at the heart of the debate over the Upper West Side middle-school-diversity plan: No parent wants it “robbing” his or her child of the chance to go to a good school — and, as parent Jason Abramson told The Post, the district just doesn’t have enough good middle schools.

That’s the real bottom line here: There’s a vast demand for good schools — across all races, ethnicities and income levels — that the system just can’t meet.

At least not without truly radical change — which is what Marc Tucker, president of the National Center on Education and the Economy, is now arguing school systems across America need: Tinkering with programs simply doesn’t work.

Of course, a wholesale rethinking is what charter schools try to do — and it’s no coincidence that so many parents opting out of their zoned school choose a charter, or that nearly 50,000 city kids now sit on wait lists, hoping a charter seat opens up.

Which makes it all the more ironic, and despicable, that de Blasio continues to do his best to stop charters from growing — even denying them the use of city classroom space that the regular public schools aren’t using.

The mayor said Thursday that he wants “more diverse classrooms that are high-quality” and that parents will want their children to attend. By far the biggest step he could take toward delivering on this would be to stop fighting the people who are delivering just that kind of classroom.